to_key = function(n)
	-- represent an integer n in base-26 using a-z
	local result = {}
	n = math.floor(n)
	local a = string.byte('a')
	while n > 0 do
		local digit = n % 26
		table.insert(result, 1, string.char(digit+a))
		n = math.floor(n/26)
	end
	if #result == 0 then
		return 'a'
	end
	return table.concat(result)
end